Blog

I’m having a difficult time finding any theory on an inverse problem I’ve come up against. Let’s say I have an unknown function $ f:[0,1] \rightarrow \mathbb{R}$ , and I know $ \int_{a}^{b} f$ for some collection $ A$ of pairs $ (a,b)\in[0,1]^2$ . I’m looking for pointers to any material that discusses condtions onRead more

Does there exists positive definite solution of homogeneous Lyapunov equation?? If yes then state the necessary and sufficient condition for the same with solution of the equation.Read more

I need to evaluate the following integral: $ $ \int_{1}^\infty dx\left({x+t^2-1}\right)^{-\frac{a}{2}}x^{-\frac{b}{2}}\left({x+r^2-1}\right)^{-\frac{c}{2}}$ $ where, $ a$ , $ b$ , $ c$ are odd and, $ t$ and $ r$ are real. Surprisingly, Mathematica is not able to compute this, nor does return any divergence issue within this interval. But on the other hand, it isRead more